Equilateral triangle

In geometry, an equilateral triangle is a triangle where all three sides are the same length and all three angles are also the same and are each 60°.
If an altitude is drawn, it bisects the side to which it is drawn, in turn leaving two separate 30-60-90 triangles

Every triangle center of an equilateral triangle coincides with its centroid, which implies that the equilateral triangle is the only triangle with no Euler line connecting some of the centers. For some pairs of triangle centers, the fact that they coincide is enough to ensure that the triangle is equilateral. In particular: